# How well do generative models solve inverse problems? A benchmark study

arXiv: https://arxiv.org/abs/2601.23238 · HTML: https://mlsanity.com/paper/2601.23238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 26 of 26)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Low-Light Image Enhancement with Normalizing Flow](https://mlsanity.com/paper/2109.05923/) (2021)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [Full-Atom Peptide Design based on Multi-modal Flow Matching](https://mlsanity.com/paper/2406.00735/) (2024)
- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [Conditional Invertible Neural Networks for Diverse Image-to-Image Translation](https://mlsanity.com/paper/2105.02104/) (2021)
- [IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures](https://mlsanity.com/paper/2103.02588/) (2021)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)
- [RNAFlow: RNA Structure & Sequence Design via Inverse Folding-Based Flow Matching](https://mlsanity.com/paper/2405.18768/) (2024)
- [LU-Net: Invertible Neural Networks Based on Matrix Factorization](https://mlsanity.com/paper/2302.10524/) (2023)
- [Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomography](https://mlsanity.com/paper/2204.06270/) (2022)
- [Digital rock reconstruction with user-defined properties using conditional generative adversarial networks](https://mlsanity.com/paper/2012.07719/) (2020)
- [A Method to Model Conditional Distributions with Normalizing Flows](https://mlsanity.com/paper/1911.02052/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Principled Approach to Unsupervised Anomaly Detection](https://mlsanity.com/paper/2609.21800/) (2026)
- [Conditional Flow Matching for ML-Based Inverse Design Problems](https://mlsanity.com/paper/2609.00863/) (2026)
- [Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems](https://mlsanity.com/paper/2610.02377/) (2026)

## Abstract (arXiv)

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a traditional Bayesian inverse approach based on a forward regression model and a prior sampled with the Markov Chain Monte Carlo method with three state of the art generative learning models, namely conditional Generative Adversarial Networks, Invertible Neural Networks and Conditional Flow Matching. We apply them to a problem of gas turbine combustor design where we map six independent design parameters to three performance labels. We propose several metrics for the evaluation of this inverse design approaches and measure the accuracy of the labels of the generated designs along with the diversity. We also study the performance as a function of the training dataset size. Our benchmark has a clear winner, as Conditional Flow Matching consistently outperforms all competing approaches.